Question: Solve for $x$ : $ 6|x - 2| + 10 = 5|x - 2| + 9 $
Solution: Subtract $ {5|x - 2|} $ from both sides: $ \begin{eqnarray} 6|x - 2| + 10 &=& 5|x - 2| + 9 \\ \\ { - 5|x - 2|} && { - 5|x - 2|} \\ \\ 1|x - 2| + 10 &=& 9 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 1|x - 2| + 10 &=& 9 \\ \\ { - 10} &=& { - 10} \\ \\ 1|x - 2| &=& -1 \end{eqnarray} $ Simplify: $ |x - 2| = -1$ The absolute value cannot be negative. Therefore, there is no solution.